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UNIVERSITY OF WASHINGTON SUBJECT Gaer"el &.11ne12r.1i:tf Z/ ti . , 21 /\/oms C"'"1 â€¢ , PROBLEM NO, _____ DATE ~l'!.4,1 ~ NA~E (r4rq/ef t l?or6:tfP UNIV111181TY 9TORII, 911ATTLII ____ _
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â€¢ â€¢ â€¢ G. E. 21 OTES A Short Course in Plane Surveying co Page 1Introduction. Page 2 Definitions. TE TS SECTION 1 MEASUREMENT OF THE LENGTH AND DIRECTION OF A COURSE Page 3Di tance, Direction and Position. 4Pacing. 4Chaining. 5Measurements on teep slopes. 6Errors in chaining. 6Stationing. 6Equations. 7Slope chaining. 8Bearings. 8Computing the bearings of a traverse. 9Magnetic bearings. 10Reading the compass. SECTION 2 MEASUREMENT OF ANGLES Page 11 Crosssectional view of the Transit. 12Horizontal Angles. 12Vertica] Angles. 12Notes on the Use and Care of the Transit. 13Verniers. 14Hints on the Use of the Transit. 15Types of Traverses. SECTION 3 TRAVERSING AND CALCULATIONS RELATING TO TRAVERSES Page 16Traversing. 16Ties. 17Locating Details. 17Triangulation. 18Obstacles. and Inaccessible Distances. 19Latitudes and Departures. 22Error of Closure. 22Angular Error of Closure. 23Balancing the Survey. 23Precision of Surveys. 23Coordinates. 24Areas by D.M.D.'s. SECTION 4 DETERMINING THE DIFFERENCE IN ELEVATION Page 27Leveling. 27Definitions. 27Engineer's Level and Level Rod. 29Using the Level, Differential Leveling. 29Hints on the Use of the Level. 30Profile Leveling. 30Precision of Leveling. 30Profile Notes. SECTION 5 TOPOGRAPHIC SURVEYING Page 81Maps. 31Contours. 31Rules Governing Contours. 32Topographic Maps. 33Classification of Surveys. 33Control Survey. 33Hand Level Topography. 34Topography by the Stadia Method. 34Inclined Stadia Sights. 35Use of the Stadia Tables. 36Stadia Field Notes. SECTION 6 LAND DESCRIPTION Page 37, 38U. S. System of Public Land Surveys. 40TraverseSection Closure. SECTION 7 FIELD PROBLEMS Page 41Map of the G. E. 21 Survey Fields. 42Regulations Regarding the Use of the Instruments. 43Problem 21C1. 43Problem 21C2. 44Problem 21T1. 45Problem 21TlA. 46Problem 21L1. 46Problem 21L2. 47Problem 21T2. 48Problem 21S1. 50Sewer Report Problem. 54Problem 21M21 (Topographic Map). 60Special Field Problem 21S2. 61Sketching Board Topography. SECTION 8 CLASS PROBLEMS Pag 62Problem 21B6. 64Problem 21L11. 65Problem 21L11.5. 66Contour Study "A". 67Problem 21TLX21. 68Stadia Tables . (Note : The student will file the problems given in class in this section after they have been returned by their instructor. Such problems must be corrected before they can be considered a part of their notes.)
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â€¢ â€¢ â€¢ I TRODUCTION TO G. E. 21 All engineers, regardless of their specializations, are often called upon to use urveying data, as well as sometimes to make the actual surveys. A surveyor is not necessarily an engineer, but all engineers are to a more or less degree surveyors, i. e., they are familiar with and can use data obtained from surveys or make the actual surveys themselves. It is obvious that in a quarter's time we can but touch upon the fundamentals of elementary surveying. The work taken up in the course is divided into two types, field and office work. Naturally the work done in the field, as represented by the field notes, is of little use until the notes are "worked up" in the office into the desired usable form. You will learn how to use the engineer's transit, level and chain for various types of work and become familiar with the office work required on the notes taken in the surveys with these instruments. Briefly the subject matter covered in the course includes differential and profile le eling, methods of measuring angles and distances, the computations of bearings, latitudes, departures and coordinates, topographic surveying and making of maps, and the U. S. system of land subdivision. The problem work in the class will be strictly individual and the same standards of neatness, clearness and adherence to the specifications will be required as in General Engineering 1, 2, 11 and 12. You will be graded upon the following: (a) class work, (b) outside work, (c) notebook (see below), (d) reports and maps, (e) quizzes and final examinations, and (f) field conduct, i. e., whether you understand your field work and whether you do your share or just stand around and let some other member of the party do it for you. I. II. The following information is given regarding your field notebook: Number all pages in the book in India ink. Put name, course, section number and instructor's name on the front cover in India ink. m. Reserve the first two pages for an index. Keep the index up to date. IV . v. See that each set of field notes is preceded by its proper title. If the problem has a number, note this number on the right hand page. Field notes are to be kept on the left hand page. The right hand page is reserved for date, weather, personnel of party, equipment locker number, sketch of survey, elevation and location of all B.M.'s, and any other data pertinent to the survey. (Use no free hand lines). VI. Use a pencil which will not cause figure! to smudge or cut into the paper. An H or 2H pencil is usually about rig ht. VII. Notes taken in the field must be recorded immediately and in the notebooks only. Do not make any erasures in the notebook. Draw a line thru an error and make a new entry neatly. If a set of notes are in error and the work rerun, draw a line across the page and mark this set "void." Notes copied by other members of a party from the notekeeper shall be marked "copy." Letters and figures should be about onehalf space high and should be written on the line. Remember that your knowledge of the use of the various instruments can come only thru practice. During each field period, therefore, individuals will change po .. sitions in the party so that every man will occupy each position at least once during the period . 1
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â€¢ â€¢ â€¢ G. E. 21 OTES DEFINITIONS Plane SurveyingThat type of surveying which considers the earth's surface as a plane, and neglects the curvature of the earth. Horizontal AngleThe angle formed by the intersection of two lines in a horizontal plane. Vertical AngleThe angle between two intersecting lines in a vertical pl ne. In surveying it is usually understood that one of these lines is horizontal. TraverseA series of lines connecting a number of e tablished points. CourseAny line connecting two points, especially in a traverse. LatitudeThe projection of a course upon a northsouth line. DepartureThe projection of a course upon an eastwest line. TriangulationThe field work necessary to determine by trigonometric computations unknown distances in a series of triangular figures. This field work consists of the determination of angles and the computations are controlled by a carefully measured base line which forms one side of one of the triangles. MeridianA line running north and south. True MeridianTrue north and south. Magnetic MeridianMagnetic north and south. (Will not be constant). lsogonic ChartA chart showing lines of equal declination for the area and date under consideration. Declination (Magnetic)The angle between the true meridian and the mag netic meridian. HubA point over which the transit is set. Usually a heavy stake containing a tack on the top to designate the point and usually set flush with the ground . StakeThis may be used for a number of purposes such as reference stake, guard stake, identification stake (station stake), grade stake, etc. It is usually driven so as to be from 6" to 12" above the ground and often in conjunction with a hub . 2
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â€¢ â€¢ â€¢ G. E. 21 NOTES SECTION 1 MEASUREMENT OF L E NGTH AND DIRECTION OF A C O URS E 1 1. It may be said that the majority of all problems in Elementary Plane Surveyin have to do with the determination of: 1. D i st a nce between two points. 2. D"rection of a line connecting two points. 3. P o s i ti o n of points (with reference to other points). 4. E evation of points (above some reference plane). and that all problems other than those specifically mentioned are related directly or indire tly to these four major items. Figure 1 repre ents two points "A" and "B" lying near t o of the building on the campus and the line conn c ing these two point ( called a course) has a 1 ngth of 76.5 feet. This 1 ng h or istan e in su eyin , unl otherwise noted, is the horizontal istanc e or the projection of this line on a horizont 1 plane. This f ct should be remembered by b inning stud nt Dist nces, u n less otherw ise noted are HORIZ ONTAL d i s tances. In some ases, it i ea. ier to measure the 0 c::.,:i FIG. 1 lope distanc e (see p ge 7), determine the vertical angle between the two point and comput the horizontal distance, but whenever slope distance are measured they hould be record d as slope distances and the vertical angle also recorded in the n e , as 246.5' @ 1215'. It i obviou th t the data given in Figure 1 give only the distance between oints "A" and "B" and that there is no relatio ship bet e these two point or the line connecting them and the two buildings. In Figure 2, this line ha been iv n additional value by howing the direction of thi line, i. e., it angular position with reference to some other line, a tual or imagin ry. In order that the direction of a line ill have a universal meaning, its angul r deviation from a NorthSouth Ii e is the method used and this deviation is called the be ri n g of the line or course. Thus Figure 2 now gives the information FIG. 2 that the horizontal di tance between point s "A" and "B" is 17 6.5 feet, an that it deviates from the north by an angle of 67 3 0' to the east or that it bears N 67 30' E, and that if we have some means of fixing the point "A" with reference to the buildings, or the buildings with reference to the line, our i nformation will be complete on erning the position of the buildings and the course with respect to each other. If the di tance of "A" f om some ea twest base line and from a northsouth base line is known as hown in Fig. 3, the poN ition of point "B" with respect to the same base lines may be found if the di tance and bearing of the course etwee is known. Also the po itions of any other points relative to this course are al o known if these other points are referenced to the same base lines. In other words, if the buildings shown are referred to these reference lines, thei position with respect to points "A" and "B" is fixe , or if it is desired to find the position of these buildings with respect to this line, the various corners of these buildings can be "tied in" with the line by determining the angular direction and disFIG. 3 I1 3
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â€¢ â€¢ â€¢ G. E. 21 NOTES tance of the various corners to either point "A" or "B". The distances from the base lines are commonly called the "coor inates" of a point and will be discussed in a subs quent section. 12. Distance. The length of any line connecting two points may be measured by: 1. Pacing. 2. Stadia. (See Topographic Surveying). 3. Direct Measurement. 13. Pacing, usually used in connection with the compass to determine the angular direction of a line, is used only in preliminary surveys due to the inherent inaccuracies of such a method. One should standardize his pace against a known distance and should take his usual walking stride. Do not attempt to take any definite di tance per pace but walk normally. Pacing on level ground will result in better results than over rough or timbered ground. 14. Direct Measurement may be made with the steel tape, usually called the "chain" or a metallic tape, the latter being a cloth tape with fine metal wires woven into the tape to give added protection against any change in length. Metallic tapes should only be used in preliminary work, or on any type of work which does not require a high degree of accuracy. The engineer's steel tape or chain is the standard m eans of measuring the length of a course if an actual measurement is to be made. This chain may be 100, 300 or 500 feet in length, the 100foot chain being the most generally used, and may be either an "adding" or "cutting" chain. An adding chain ha an extra foot past both the zero and 100foot ends each divided into tenths, while a cutting chain has the first and last foot divided into tenths. In both cases, the remaining part of the chain is marked only at the foot marks, 1, 2, 3, 55, 56, 57, etc. Whenever using a chain for the first time, or a different chain than usually used, always note the zero points and whether the chain is an adding or cutting chain. Note: This applie to metallic tapes as well, for a very common mistake is to read the zero point wrong, it being u ually at the end of the ring. 15. In Chaining, the head chainman always carries the zero end of the chain ahead (either uphill or do nhill) and should not overrun hi s point, i. e., always keeping the chain strung out behind the head chainman, and no t extending ahead of the final point. The method of mea uring betwe en two points with an adding and a utting chain i hown in Figure 4. Note that the adding chain will always read the D1stooce = 55; dcld a 6 ::: 55. 6' 'i1cltlino C@in ,, 1 A "odd" ZRo' , .. Cuttin9 Chain,, l f I I I B FIG. 4 12
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â€¢ â€¢ â€¢ G. E. 21 nearest full foot mark direct, with the tenths to be added to that reading while the cutting chain will always read one foot greater than the actual nearest foot from which must be subtracted or "cut, " the di tance the divided portion of the chain overruns the point. 16. C hain i n g o n Steep Slopes. Inasmuch as the distance between any two points such as "A" and "B" is the horizontal distance, chaining down or up a hill often in volves the procedure of "breaking chain" a shown in Figure 5. FI . 5 Wh n "breaking h in" in chaining uphill or down hill, the chain is held horizontal at each step. The use of a hand level will aid in making certain that the chain i level. The downhill end of the chain is held at some convenient height, usually not above eye level and the plumb bob is su pended from the desired graduation on tne chain to locate the point on the ground which is then marked with a chaining pin. This pin is picked up by the rear chainman when the next point has been set. The rear chainman should call out the distance as he reads it on the chain for each "break," the head chainman repeating and adding it to the previous distance. Beginners usually should mark down the breaks in the back of their field book, but practice will soon allow the head and rear chainm n to carry the distances "in heir heads," one checking the other. 17. Alternate Method of Breaking Chai n for Distances Over 100 Ft . Many authorities recommend the carrying of the chain to its full chain length by the head chainman who then returns to some mark on the chain which will give him an eyelevel reach for his plumb bob tring when the chain is horizontal, where a pin is set and the distance called out to be repeated by the rear chainman. The rear chainman then comes up to the pin and holds the same distance as read originally by the head chainman who now has gon ahead for another eyelevel plumbing. This i s continued until the zero mark of the chain is reached. This method has the advantage that the "breaks" of ious hort distances mea ured are carried by the chain so that when the end of th chain is reached, another one hundred feet has been measured, without the nece ity of carrying these broken distances "in one's head" thus eliminating errors in adding or forgetting a distance. t has the disadvantage of being more difficult to get the proper pull on the chain when grasping some point in the middle of the chain. Ina mu h as the pin pi ked up by the rear chainman ordinarily represent a hundred feet, the pins should be redi tributed according to the total distance chained in terms of an even hundred fe t after breaking chain regardless of which method is employed. As a general rule distances measured downhill will give more accurat re ult than those mea ured uphill. I 6 5
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â€¢ â€¢ â€¢ G. E. 21 NOTES 1 8. Errors in Chaining. Erro 1S in chaining may be due to any or several of the following reasons: 1. Chain not held horizontal. 2. Chain not pulled tighttoo much ag. 3. Chain not standard length. 4. Chain out of alignment. (The rear chainman should always "line in" the h ad chainman. 5. Inaccuraci s in p]umbing and setting pins. 6. Variation in length due to extremes in temperature. 7. Reading or recording distances incorrectly. (Dropping a full chain (100 ft.) is a common error). 8. Effect of wind. 19. Care of the Chain. The chain is made of tempered steel and will not stand being bent in a small radiu and if pulled tight in an endeavor to straighten out any kinks will readily break. It should be "done up" by "throwing" as directed by your instruc or and always put away in this form. It should never be "done up" in a "cartwheel" and alway hould be wiped dry if expo ed to moisture. If, in undoing, a chain becomes tangled, one must take the time to straighten it out without undue tension which might cause it to break at some point where a kink suddenly devel ops. 110. Stationing. On long traverses such as used in highway, railroad, irrigation canals, mining, municipal and kindred surveys, it is customary to establi h the 100foot points, i.e., set a stake every even hundred feet. If 1 of Figure 6 represents the beginning of such a traverse, a stake would be set at each 100foot mark and a hub with a reference stake at each angle point, A, B, C, D, E, F,etc. To designate these angle points by the letters A, B, C, etc., tells nothing of their location with respect to the 100foot stakes or the other angle points of the traverse. To facilitate the marking of both the 100foot stakes, and the angle points, the 100foot stakes are called stations, and the distances between 100foot stakes become plus stations. Thus the second 100foot stake would be called and marked Sta. 2 + 00, the initial starting point Sta. 0 + 00, and the first angle poin becomes Sta. 2 + 14.6 instead of point "B" as shown in 2 of Figure 6. From the above it is obvious that a station designates a point and is not a disA tance. The use of station , however, does give some information concerning distan ces which is not po sible when the points are given a letter designation. Referring to 1 2 I I~ tr..;, / I") 3 / II I o O * ;. FIG. 6 1 and 2 of Figure 6, we ee that the stationing of points " " and "D" is 3 + 65.0 and 4 + 85.2 and that if we subtract 3 + 65.0 from 4 + 85.2 we have the di tanc e between these two point or 120.2 feet. Likewise the stationing tells us that the e two point are 365.0 and 485.2 feet from the starting point. This i true provided there is no EQUATION between these points. In determining the distances between any points from their stationing, one must che k the data to find out whether one or more equa ions exi t b tween the points in question. Referrin aoain to 2 of Figure 6 we note that ther is an equation betwe n 3 + 65.0 and 4 + 85.2 reading thus: 3 + 95.0 = 4 + 00. It may be that he kin the field work an error wa di c ove "ed in mea urin the distance between and D and that this di tance hould be 115.2' instead of 120.2'. â€¢ I8 6
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â€¢ â€¢ â€¢ G. E. 21 Now it should be remembere that all stak s are in, the recording in the fieldbook and perhaps a good share of the office work done, all based on this incorrect di tance, and that to make the necessary corrections in the field and office would inol con iderable work. If at the point the error occurred, the correction is made and made only at that point, this added work will be eliminated. This is done by placing an equation 3 + 95.0 = 4 + 00.0 at this point. It simply means that this point has two stationings, the first reading for all points behind it and the second for all points ahead. The correct distance between Sta. 3 + 65.0 and 4 + 85.2 now becomes [ (3 + 95.0) (3 + 65.0)] + [ (4 + 85.2) (4 + 00.0)] or 30.0 + 85.2 = 115.2 f et. 111. Equations have another valuable use beside that of correcting errors. Sup pose as a result of the studies made from field data it is desirable to relocate the line between B and E by the elimination of the loop as shown in 3 of Fig. 6 and that the distance between B and E on the new straight location was 320 feet. This can be taken care of without changing the tationing of the remaining part of the line if an equation is placed at either B or E. If placed at E, E will now possess two stationings, 5 + 34.6 and 7 + 35. , the first for all points behind and the second for all points ahead, and at this point (E) there would be placed the equation 5 + 34.6 = 7 + 35.8. The first figure of this equation was obtained by adding 320 feet to the original stationing of point B. The total distance from A to F over the revi ed line now be comes [ (5 + 34.6) (0 + 00)] + [ (8 + 81.3) (7 + 35.8)] or 534.6 + 145.5 = 680 feet instead of 876.3 feet for the old line as shown in 2 of Figure 6. 1 12. Slope Chaining. In chaining over rough ground, especially when a 300 or 500foot chain is available, more accurate results will be obtained if the slope di tance is measured and the horizontal distance computed. The chain is stretched from the axis of the transit directly to the top of the hub and the vertical angle is read. See Figure 7. Horizontal Distance (DC) = (Cosine 6) (Slope Dist. DB) . FIG. 7 111 7
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â€¢ â€¢ â€¢ G. E. 21 NOTES 113. Direction of a CourseBearings. The direction of any course is designated by the horizontal angle that the course makes with the meridian (a northsouth line). This deviation from the meridian is called the bearing of the course, and its position left or right of the meridian is shown by the proper eastwest designation. Bearings are measured from the north to either east or west and from south to either the east or west, hence, a bearing can never be over ninety degrees. Figure 8 illustrates the method of computing bearings. Thus: Angular deviation of 12 is 50 from the north to the east and the bearing becomes N. 50 00' E. Angular deviation of 13 i 2 50 from the south to the east and the bearing be comes S. 50 00' E. Angular deviation of 14 is 60 from the south to the west and the bearing becomes S. 60 00' W. Angular deviation of 15 is 45 from the north to the west and the bearin b comes N. 45 00' W. Note: When the term "bearing" is used it is understood to be the "true bearing" or the angle to the east or west which the course makes with a true north and south line. 114. To Compute the Bearings of a Traverse. If it is desired to compute the bearings of the closed traverse ABCDA (designated a "closed traverse" because it makes a closed figure) from the measured angles as shown in Figure 9, the simplest and most foolproof method is to make a sketch of the traverse, using only approximate angles, and at each angle point erect a small north pointer as shown. This presents a clear picture of the setup and allows one to see in what quadrant the bearing will be. The computations would be as follows: , Bearing of the cour e AB is given as N. 50 00' E. 5 FIG. 8 FIG. 9 Bearing of BC = 180 (1 + 67 00') = 180 117 = S. 63 00' E. Bearing of CD = 102 2 = 102 63 = S. 39 00' W. Bearing of DA = 180 (a + 77) = 180 (89 + 77) = N. 64 00' W. Check bearing of AB = 114 rb4 = 114 64 = N. 50 00' E. It is obvious that the bearings must be computed from some line of known bearing and will be in error if the original bearing is in error. In some cases where a known bearing is not available, one of the courses may be given an assumed bearing to start the computations; these bearings to be corrected later if necessary . I13 8
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â€¢ â€¢ â€¢ G. E. 21 NOTES 115. Magnetic Bearings. The m gnetic needle possesses the property of pointing in a fairly fixed direction, the Magnetic Meridian, and the angle which the magnetic needle makes with the true meridian is called the declination of the needle ("Variation" in navigation). The needle of the compass, however does not constantly point in the same direction as there are small variations of the declination known as the Secular, Daily, Annual and Irregular. The declination of the needle also varies in different parts of the country, and if lines are drawn on a map so as to pass through all points where the declination is the same at a given time, we have what is called an isogonic chart. These charts are published every five years by the United States Coast and Geodetic Survey. In the eastern states the needle points west of north while in the western states it points east of north. For 1930, the line of zero declination passes through South Carolina, Ohio, Indiana, and Michigan. 8 FIG. 10 FIG. 11 Dec. = Declination = True Bearing A = True Magnetic Bearing A1 = Observed Magnetic Bearing Figure 10 represents the position of a course AB with respect to the true north and magnetic north for a declination to the east. If this declination was 24 E., the magnetic bearing (always written with the adjective "magnetic" to distinguish it from a true bearing, or "Bearing") would be N. 26 00' E if the deviation of the line from the needle (A) is 26 degrees. The true bearing of the line AB would, of course, be equal to 26 + 24 or N. 50 00' E. As the needle is always affected by masses of iron and sometimes by electric machinery near the compass, a compass bearing may not read the true magnetic bearing. Figure 11 illustrates such a condition. If in this case the local attraction is 2 degrees to the west, the needle is drawn that much to the west from its normal declination. If we consider the normal declination is again 24 degrees east of true north, and the observed magnetic bearing (A1 ) to be N. 50 00' E., the true mag netic bearing would be N. 48 00' E. and the true bearing N. 72 00' E. The above may be summarized in the following steps, which if carefully followed will greatly facilitate the correction of observed bearings to obtain true North bearings. 1. Draw the line and the compass needle in the observed position which shows the observed bearing angle. 2. Correct the position of the N compass needle for local attraction, if any. 3. Correct this new position of the compass needle for magnetic declination, which will bring it to the true north position. 4. Read the true Bearingin the proper quadrant . I15 9
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â€¢ â€¢ â€¢ G. E. 21 NOTES 116. Reading the Compass. A bearing is always read from the North end of the needle. The "N" (or "S") and "E" (or "W") will be those letters which appear on either side of the needle. In order to have these letters read correctly, the "E" and "W" are reversed from their natural position. The zero of the scale always is along the line of sight. 2 3 FIG. 12 Referring to Figure 12 above, 12A indicates the position of the compass with the line of sight along the magnetic meridian 12. In 12B the transit's (or compass) line of sight is along the line 13 for which the bearing is desired. Reading the north end of the needle we find the angle to be 45 degrees and the letters "N" and "E" to either side of the needle, giving the bearing as N. 45 00' E. Figure 12C gives the position of the compass and needle for the line 18 which has a bearing of S. 45 00' W . I 16 10
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G. E. 21 NOTES â€¢ â€¢ Piece Piece No. No. 2. Sunshade. 48. Plumb Bob Cap. 6. Cross Hair Frame. 49. Spindle Release Spring. 8. Pinion Head. 50. Compass Glass. us. Axis Clamp complete. lSlB. Plunger for Plate Tangent. 17. Tangent Screw. lSlC. Plunger for Clamps. 18. Vertical Circle. 56. Cap for Clamps. 19. Standard Level Housing. 57. Clamp Screw. 21. Vertical Circle Guard. 62. Standard Cap Screw. 25. Plate Level Housing. 65. Axis Clamp Screw. 26. Plate Tangent Screw. 75. Shade Glasses. 30. Vernier Shade Bracket. 82. Plate Clamp Screw. 30A. Vernier Shade Bracket Screws. 815. Acorns for Axis. 31. Shell for ompass Glass. 86. Guard Screws. 34. Compass eedle. 87. Tangent Spring. :17. Plate Clamp complete. 88. Chain for Pl um b Bob . :18. Collar. 89. Vernier Cover Glasses. 40. ower Clamp complet 90. Dust Cap for Telescop e . 42. Leveling Screws. 94. Collet Fastening Screws . 43. Leveling Screw Cups. 95. Collet. â€¢ 46. Base Plate. 112. Collar Fastening crews. 47. pindl ut. ourtesy of A . Lietz Co. , San Francisco 11
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â€¢ â€¢ G. E. 21 NOTES SECTION 2 MEASUREMENT OF ANGLES 21. Angles are mea ured by the Engineer's Transit and may be divid d into the two major groups of horizontal angles and vertical angles. The former may be defined as the angle formed by the intersection of two lines in a horizontal plane while a vertical angle is the angle between two intersecting lines in a vertical plane, one of which is horizontal. Horizontal Angles. The angle made by any two intersecting lines may be measured by any one of the four foil owing methods: 1. Interior Angle. N 2. Deflection Angle. (Right or Left). 8. Azimuth from the South. (Clockwise) 4. Azimuth from the North. (Clockwise) . Note: In G. E. 21, azimuths will be considered as measured from the north. Referring to Figure 13, it will be noted that a deflection angle is the angular deviation between the first course extended and the second course, and can be either right or left with a maximum value of 180 degrees. An azimuth is the angular deviation of a course from the north end of the meridian measured clockwi e with a maximum value of 360 degrees. FIG. 13 1. Interior Angle 2. Deflection Angle [Right (R) or Left (L)] 3. Azimuth from the South (Clockwise) 4. Azimuth from the North (Clockwise) 22.Vertical Anglea. Vertical angles are read both up and down and should be designated by a plus or minus sign to designate the direction of the deviation from the horizontal. Inspection of the transit will show that in taking vertical angles, the vernier remains fixed while the vertical graduations move with the telescope, while in turning a horizontal angle, the vernier moves with the turning of the transit. Vertical angles are used in slope chaining (see Figure 7) and extensively in stadia work. 23. G neral Notes on the Use and Care of the Transit. The Engineer's transit is an instrument of precision designed primarily for the measuring of horizontal and vertical angles. Being an instrument of precision it should be handled accordingly. See that the tripod legs are firmly set in the ground, that the leveling screws are firm but not jammed, that the instrument is centered on the sliding head when put away, and wiped free of all dirt and moisture when returned from the field. Briefly the transit consists of an outer graduated plate and an inner plate to which a telescope is a tached, and with a zero point marked on the inner plate beneath the eyepiece of the tele cope. Both plates revolve in a long collar supported on a tripod by means of four leveling screws. The outer pla e is graduated from zero to 360 in a clockwise direction, and in a counterclockwise direction. The latt r or inner set, may be divided from zero to 360, from O to 180, then back to zero, or from O to 90 then to 0, etc., and one should inspect a new instrument before starting work in order that erro 1 in reading the angles will not occur from this cause. The newer instruments have both the outer (clockwise) and inner (counterclockwise) graduations divided from zero to 360. As your instructor will personally explain the various features of the transit to you in the field, no more detailed explanation â€¢ will be given here. 21 12
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â€¢ â€¢ â€¢ 24. Vernier s. The v rnier i a de ice for determining the subdivision of the smallest di v i ion of the ale and as the transit's outer plate has two scales, the vernier i a "double vernier" in order that both inner and outer scales may be read to the smalle t divi ion, u ually to minute . The vernier is read in the same direction as the cale was read and the correct subdivision or minute will be where a line on the vernier exactly matches or coincides with a line on the scale. If the scale is divided into degrees and half degrees, the vernier must of course be divided into 30 parts, each part repre enting one minute. If on the other hand, the scale is divided into degrees and onethird degrees (20 minute ) the vernier will be divided into 20 part . Since the ernier (in horizontal angles) moves with the telescope, the angle must be read in the same direction that the telescope has moved, and the vernier likewise i n the same d irection. Read the degrees and parts of a degree, either onehalf or onethird that the index has pa ed over, then follow ahead in the same direct ion on the vernier until as stated above, one of the line on the scale matches a line on the vernier, the latter giving the number of minutes to add to the degree and part of a degree read from the cir le or scale. Referring to Fig. 14, if one is reading the outer cale we find that the Index "A" of the vernier has moved to th VERNIER A right ( ounter clockwi e) and ha pa ed the 9 mark on the scale and following to the right on the vernier we find that the 16 line on the vernier matches a line on the ale; the angle therefore is 9 16'. If the inner scale is being read, we find that the index "A" has moved to the left and has passed the 3500 mark and continuing on to the left on the vernier, we find the 14 mark on the vernier coinciding with a mark on the scale and the angle is 3501,/2 14 ' = (360 30' + 14') or 350 44'. Common M istakes in R eading Angles. 1. Reading the wrong half of a double vernier. 2. Forgetting to add the ubdivision of the scale to the vernier reading, as in the second case above by recording the angle as 350 14'. 8. Reading the wrong side of the cal e, a 10 0 instead of 9 in the first reading above, and as 3 6 9 instead of 3500 in the second case. 4. Reading the wrong scale. Get in the habit of estimating the angle as a check and in noting which cale to read as you start to turn the angle . 24 18
PAGE 16
â€¢ â€¢ â€¢ G. E. 21 NOTES 26. Hints on t e Use of the Tran i â€¢ 1. See that the tr n it is centered on the tripod before setting up. 2. See that the transit ha a convenient height, with the tripod head approximat ly level. 3. See that the t ipod legs are firmly pressed into the ground. 4. The leveling screws should be firm, but not jammed. 5. The plumb bob should never be more than on ehalf inc h above the point. 6. Do not place your hands on the tripod when taking a sight. 7. Look over the top of the telescope to get the approximate line of sight to the desired point. 8. In turning an angle, estimate its value first, and as you start to turn it, note whic h scale you are reading. 9. Sight on a pencil for short sights, on the plumb bob string for short and moderate ights when you cannot see a pencil because of the lope of the ground or intereference by grass, etc., and at a range pole only on long sight . 10. Be careful not to use the wrong clamp or tangent screw. 11. Sight always as low as possible on a pencil, plumb bob line or range pole, using the intersection of the vertical hair and the middle hair. Do not use the stadia hairs (the upper and lower of the three horizontal hairs). 12. In G. E. 21, if you have a transit with two verniers, use the "A" vernier only, forget that there is a "B" vernier. 13. Save your lungs and bystanders' ears by using the following signals whenever possible: "Right" or "Left" Extend the arm in the direction of the desired movements, the right arm for a move to the right, the left for a move to the left. A long slow movement, to designate a long movement, a short quick motion for a short movement. "Plumb the Rod" Hold the arm vertically and move in the direction the rod should be moved to be plumb. "Give a Sight" Hold the arm vertically above the head. "Set a Hub" or "Establish a Turning Point" Hold the arm above the head and wave in a circle. "Give Line" (By a rodman) Hold the rod horizontally in both hands above the head, then bring it down and hold vertically. "Turning Point" or "Bench Mark" (By a rodman) Hold the rod in a horizontal position above the head and then bring down on the point. "Wave the Rod" The instrumentman should hold one arm above the head and move it from side to side. "All Right" Hold both arms to the side horizontally and raise and lower the forearms rapidly . 26 14
PAGE 17
â€¢ â€¢ " â€¢ G. E. 21 NOTES 27. Types of Traverses. Figure 15 illustrates three common methods of measuring the angles of a traverse, (1) by interior angles (See Field Problem 21T1), (2) by B FIG. 15 deflection angles (Field Problem 21T2), and (3) by azimuths. Interior angles are measured independent y of each other, i.e., each setup is an individual problem and has no bearing on the previous setup. Briefly the procedure is as follows: Set up over any point, say A (see 1 of Figure 15,) clamp the plates at zero with the upper clamp, backsight on the point behind, D, and clamp the lower clamp, then loosen the upper clamp, sight on the point ahead, B, and read the angle. This angle should be doubled as follows: With the angle as read left on the plates, loosen the lower clamp, turn the telescope to the backsight D again, tighten the lower clamp, loosen the upper clamp and sight on the point ahead B, read the angle and divide by two for the correct angle to record, or what you actually do is read the same angle twice, adding the first reading to the second and take the average of the two. As a check, estimate the angle by the eye before taking the reading. The procedure in making a deflection angle survey is given in Field Problem 21T2. 28. Survey Using Azimuths. (3 of Figure 15). A suming that the azimuth of AB is known, say, 50 degrees: FIRST METHOD. Set up at B, backsight on A with the plates clamped (upper clamp) at 180 + 50 (back azimuth), tighten the lower clamp when on A, loosen the upper lamp, sight on C (remember the clockwise motion) and read the azimuth of BC. Do likewise at Stations C and D. SECOND METHOD. Invert the telescope and backsight on A with the plate clamped (upper clamp) on the azimuth of A (50), tighten the lower clamp when on A, plunge the telescope, loosen the upper clamp, sight on C and read the azimuth of BC. Repeat at C and D. The disadvantage of this method is that if the axis of the telescope is not perpendicular to the line of sight ( error of collimation) this error will enter each azimuth. If in either method the azimuth of AB is not known it may be assumed or taken from a compass reading of the course AB, and corrected later. 29. Completion of Survey. To complete the surveys as illustrated in Figure 15, the lengths of each course should be measured, and the bearings computed from the horizontal angles as read. It is obvious that in order to complete the bearings, the bearing of one of the sides must be known, assumed or determined from an angular measurement from some other line of known bearing. 27 15
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â€¢ â€¢ â€¢ G. E. 21 NOTES SECTION 3 TRAVERSING AND CALCULATIONS RELATING TO TRAVERSES. 31. Tr versi g. Tra er ing is the general term given to the process of running a transit traverse and differ but little whether the angles are interior angles, deflection angles or azimuth . The choice of points for the traverse will be determined by the purpo e for which the survey is run, remembering that the traverse is but the framework upon which to build. If the survey is a hydrographic survey the points will be cho en which will give a good view of the areas to be sounded; if for a topographic map, stations will be used which will give sights over the desired area, and if for a highway or canal will follow the general route decided upon. The traver e may be an open or continuou traverse similar to Fig. 6 , from a few hundred feet in length to many miles; a simple closed traverse which comes back to the starting point, or a combination of closed traverses as shown on page 16. Any point in uch traverses over which a transit is set in order to read an angle is called a transit station, and such a point is usually a tack set in a hub driven flush with the groun accompanied by a reference stake upon which is printed the stationing, number or letter designation of the hub. Such points are often of a more or less permanent nature, and should always be referenced or "tied in" with other points or permanent objects so that they may be either reset if removed (as during the process of construction) or found if the guard stake is removed. Such ties should be recorded on the field notes. Figure 16 illustrates two methods of making such a tie. Fig. 16: 1. Common method of tying in two points so that they may be quickly found if the guard stakes are removed, distances measured only . 2. One of several methods of tying in a point so that it may be reestablished if moved, distances measured only. All hubs should be so referenced that any stranger may be able to quickly locate all points if in possession of the field note book. This is a portion of the field work often neglected by beginners. Distances in traversing, unless the traverse is of minor importance, will be measured with the chain, with the best results obtainable when slopechained with a 300 or 500foot chain. (See Fig. 7). This is es. pecially true in rough country . 1 2 FIG. 16 3 1 16
PAGE 19
â€¢ â€¢ â€¢ G. E. 21 NOTES 32. Locating Details. If the traverse has been run as a base for making a map, several methods are available in determining the position of various objects with reference to one or several courses of the traverse so that they may be quickly and accur. ately plotted. The more common of these methods are given in Figure 17. 1 2 5 FIG. 17 1. By measured distances and angles. 2. By the intersection of two lines. (Angles only read). 3. By perpendicular offsets from the line. 4. By swing offsets; one offset an extension of the side of the building. 5. By swing offsets. 6 6. By oblique offsets to the line where both offsets are extensions of two of the sides of the building. This is an approximate method and can only be used on small scale maps where the fact that the line and one side of the building are not parallel will not be evident on the finished map. Triangulation. Triangulation is that method of running a control traverse, where the majority of distances are computed rather than chained. Usually but one distance is measured, and that , with every precaution available, and from this base line and the carefully read angles at the various triangulation points, the other distances are computed. A simple triangulation scheme is shown in Figure 18, with angles read at points c =A, B, C, and D. FIG. 18 3 2 17
PAGE 20
â€¢ â€¢ â€¢ G. E. 21 NOTES 34. Obstacles and Inaccessible Distances. In Figure 19, two methods of prolonging a straight line are given. Assuming that it is desired to extend the line 13 to 7 and beyond, make equal rightan led offsets at 1 and 3 and extend the line 24 thus formed on ahead to 6 and 8. From 6 and 8 make the same equal rightangled offsets and locate points 5 and 7 which will be an extension of the line 13. If the stationing is being carried along the line, the 90 angles at 3 and 5 should be determined with the transt. The degree of precision required of the survey w i 11 determine whether or not the other 90 offsets should be measured with the transit. The second method of prolonging the line past the same obstacle is to go around the object with an equilateral triangle (in2 4 6 8 terior angles all 60 and sides the same {i):ttlength). Set up the transit at "A", turn off l 1 an angle of 120 from point 1, measure a I I distance to "C" which will clear the obI 10J~,,,. A 1 ject. Set up at "C", turn 60 from "A" and measure the same distance to "B" as was measured from "A" to "C". The distance from "A" to "B" will be the same. Set up at "B" and turn 120 from "C" and set up point 7. The line "B"7 becomes the exten sion of the line 13"A" with the stationing now known. C FIG. 19 35. The determination of an inaccessible distance is primarily a problem in triangulation. Two methods are given in Figure 20 for the case where it is possible to sight along the line. Set up the transit over point "B", turn off 90, set "A" and chain the distance AB. Set up over A and measure the angle BAD. BD = AB tan BAD A check can be made by measuring the angle BDA . In the second method, the angle turned off at station "B" is also 90, but the angle at "A" is made definitely 90 from D and the point "C" established on the line DB extended. AB and BC are chained. CB _ (AB)2 AD FIG. 20 The bearing and length of an inaccessible course may be determined by making this distance one side of a closed traverse. Computing the latitudes and departures of the known sides (see p. 19). The latitude and departure of the unknown side is the algebraic sum of the latitudes and departures of the known sides. Knowing the latitude and departure of the unknown course, its length and bearing may be readily computed . 34 18
PAGE 21
â€¢ â€¢ â€¢ G. E. 21 NOTES 36. Latitudes and Departures. The latitude of any course is the distance north or south that the course goes, or the projection of the course on a northsouth line. The departure of a course is the distance east or west that the course goes, or the proj ection of the course on an eastwest line. In Figure 21, the latitude of the course AB is equal to the side AC of the triangle ABC, and the departure equal to the side CB. As the triangle is a right triangle, and the angle CAB is determined from the bearing of the course we have the relationship that: The Latitude of any Course = (Distance of that Course) (Cosine of the Bearing). The Departure of any Course = (Distance of that Course) (Sine of the Bearing). ~fa:7/'"~re (E) ~=====B N I i ' ~, I ~I : FIG. 21 North bearings will give north latitudes, south bearings south latitudes, east bearings east departures and west bearings west departures. The computation of the Latitudes and Departures of a closed traverse is a step in (a) the determination of the Error of Closure, (b) the determination of the Coordinates of the various angle points of the traverse and (c) the computation of the Area inside the boundary of the closed figure. 37. Form of Computations. Figure 22 represents a traverse of five sides with a total length of 27 40.0 feet. Facing this figure is given the form to be used in G. E. 21 for computing and arranging the results of the computations. The lower form (Standard Computation Form G. E. 21) is to be used for the computation for the latitudes and departures of the traverse, and the upper form (Standard Coordinate Table) is the usual arrangement for properly placing the latitudes and departures for the computation of the error of closure and the coordinates of the various points. Extra sheets of both of these forms are included in the back of these notes for use in class and field problems. , 36 19
PAGE 22
Standard Coordinate Table Sta. Dist. AGLE BEAR! G LATITUDE DEPARTURE COORDINATES N s E w Elev. ()t(10 . 73 '.3.3 027' 217.36 7.73 J+91.3 :397.2 /\1631135 76.7/ 7+fl5 . 9 s 9~_q3 /4t/ , q 2219~.9 449.1 27i41/.0 :::01= â€¢TANDARD COMPUTATION FORMâ€¢G. It. 21 COURSE C DISTANCE BEARING LATITUDE LOG. LAT. 5 LOG. COS, 2 LOG. DIST. I LOG. SINE, 3 LOG. DEPT. 7 0 â€¢ â€¢ â€¢
PAGE 23
â€¢ â€¢ LATITUDES, DEPARTURES AND COORDINATES 14+1'1.t ~~~~a=!::!~~.I!___:~~~s.=:=Y~&a5i~~e:...::b.=,ne~L.I.L38 The Latitude of any Course = (Dist.) (Cosine Bearing) The Departure of any Course= (Dist.) (Sine Bearing) The Coordinates of any point= the algebraic sums of the Latitudes and Departures respectively from a point whose Coordinates are known or assumed. FIG. 22 â€¢
PAGE 24
â€¢ â€¢ â€¢ â€¢ G. 'Jn. 21 NOTES 39. Error of Closure. Referring to Fig. 28, it is obvious that if there is no error in the field work (both angles and distances) point x' should coincide with point x, i.e., the final point as measured around . . cl. ~d the traverse should come back to the f 7 exact starting point. If this is true, then the total distance traveled no . rth L~1 2 should equal the total distance travN ~2 eled south, and the distance traveled " east should balance the distance s , traveled west, or L1 + L, = L2 + La ':J l.X and d 1 + d2 = d8 + d, where L1 is.the I\ latitude of course 1, and d1 the depar4 ture of course 1, or The North LatiL4 , LJ tudea ahould equal the South LatiL I tudea and the East Departures should d
PAGE 25
â€¢ â€¢ â€¢ G. E. 21 NOTES 311. Balancing the Survey. This expression is given to the process of distributing the error of closure among the latitudes and departures to make a "balanced survey." Of course if the error of closure is beyond the limits of the degree of accuracy of the work at hand, the field work must be checked. If the error is small, divide it up among the various latitudes and departures "by eye," there being no necessity to depend upon any rule for an error less than a couple of feet for a large sized tract. If the error is larger, but still not too large to necessitate checking the field work, use the following rule : titude H Length of][ Total Error in (Lat.) ] Correction to any eparture That Side . (Dept.) Total length of traverse 312. Precision of Surveys. The following specifications for traversing are suggested. CLASS 1. Preliminary surveys, horizontal control for topographic surveys of minor importance. Allowable angular error of closure 1'80" yll, (n = number of angles read) Allowable error of closure l,~OO CLASS 2. Most land surveys, highway location work and ordinary topographic surveys. Allowable angular error of closure 01' .../n 1 Allowable error of closure 8,000 CLASS 8. Most city surveys of important boundaries, and for control t.raverses for extensive topographic surveys. Allowable angular error of closure 80"v1n 1 Allowable error of closure 5,000 CLASS 4. For most precision surveys. Allowable angular error of closure 15" VD 1 Allowable error of closure 10,000 318. Coordinates. A traverse is the framework of the survey and as such should be plotted with the utmost care. Experience has shown that it is not possible to plot the angles with sufficient accuracy using a protractor and scale, and the coordinate method is the most accurate as well as the most practical method of plotting the traverse. Inasmuch as the latitudes and departures have already been computed in order to determine the error of closure as a check on the field work, the computation of the coordinates from these latitudes and departures becomes a simple task. If the field work is not to be tied in with other work, the base lines, one eastwest, the other northsouth may be assumed, making a choice so that all the points in the traverse will fall in the same quadrant. In the majority of cases this quadrant will be chosen as the northeast quadrant. If the survey work is to be tied in with existing surveys, a tie should be made to some point whose coordinates are known and its base lines used. Referring to Figure 19, if the coordinates of Station O + 00 are known or assumed to be N.885.25 and E.642.78, it means that this point is 835.25 feet north of an eastwest base line and 642.78 feet east of a northsouth base line. If the course from Station 0 + 00 bears S. 56 27' E. and its latitude is 217.86 and departure 327.78, Station 3 + 98.3 will be 217.36 feet south and 327.78 feet east of Station O + 00 and its coordinates will be (835.25) (217.86) = N. 617.89 and (642.78) + (827.78) = E.970.56. Coordinates are sometimes called "Total Latitudes" and "Total Departures" and the first figure of the two as they appear opposite any point is the distance north or south from the base line, and the second figure the distance east or west from the base line. The letter in front of the coordinates designates the direction from the base line. Referring to Station O + 00 again, its coordinates a11 28
PAGE 26
â€¢ â€¢ â€¢ G. E. 21 NOTES should be preceded by the letters N and E and should read N.835.25, E.642.78 indicating a point in the northeast quadrant 835.25 feet north of the EW base line and 642. 78 feet east of the NS base line. In such a case all courses having north latitudes will have that latitude added to the north coordinate of the previous point; south latitudes will be subtracted; east departures will be added to the east coordinates and west departures subtracted to give the coordinates of the next point. In plotting by coordinates the coordinate lines should first be very carefully plotted and checked, and as each point of the traverse is plotted, the distance between any two points which represents the course as surveyed, should be scaled and checked against the chained distance. Courses may be plotted directly from the latitudes and departures if desired, but this method is not recommended over that of assumed coordinates. 314. Areas Without Anglea. A traverse may be run using only a chain as shown in Figure 24, although the position of this traverse with respect to the north cannot be determined. It is possible however to compute the area enclosed by the boundary of the traverse inasmuch as in chaining it was necessary to divide the area up into vari ous triangles. More often, however the traverse will be a normal traverse run with the transit and chain, and the latitudes and departures computed for the purpose of determining the error of closure and for computing the coordinates. A closely related step is to use the 9 latitudes and departures to com. Lpute the area (if desired) by the 5 :r Si0tn .A method known as Double Meridian 2 Distances. FIG. 24 315. Areaâ€¢ by D.M.D'a. The area of a closed traverse may be computed by the use of double meridian distances in which the meridian is considered as passing through the most westerly point of the traverse ; the meridian distance being the distance from the middle point of any course to this reference meridian, measured at right angles to the meridian. A series of geometric figures are formed from which it is possible to determine the area of the enclosed portion of the traverse. No attempt will be made here to go into detail concerning this method and it is presented as a tool to use in the determination of areas after the latitudes and departures of a traverse have been computed. The student is referred to the material on page 26 and the explanation given in any standard text on surveying. The procedure for determining the area of a closed traverse by the D.M.D. meth od is outlined in the following rules: 1. Determine the most westerly point of the traverse and consider that a meridian is passed through this point. 2. The D.M.D.'s of the two courses adjacent to this reference meridian are equal to their respective departures. (NOTE: Start the calculations of the D.M.D.'s from the most westerly point. proceeding in the direction in which the survey was run. The last computed D.M.D. should equal the departure of the last course, which gives a check on the computation . 314 24
PAGE 27
â€¢ â€¢ â€¢ G. E. 21 NOTES 3. Compute the D.M.D. of each course as follows: The D.M.D. [ D.M.D. of ] [ Departure ] [ Departure ] of any = previous + of previous + of new course course course course All All W. departures W. departures positive positive negative negative 4. Multiply the D.M.D. of each course by its corresponding latitude. North latitudes will give north areas and south latitudes will give south areas. 5. Subtract the areas (North and South) and divide by two. This will give the area in the same units squared in which the linear distances were measured, i.e., if the distances were measured in yards, the area will be in square yards, if in feet, the area will be in square feet. 316 . Example of the Computation of theArea of a Closed Traverse by the Method of D.M.D.'a. Let it be assumed that it is desired to find the area enclosed by the traverse given in Figure 19. It is obvious that Station 22 + 90.9 is the most westerly point, so a meridian is considered as passed through this point, and the computations are figured in the direction in which the survey was run, i.e., clockwise. Station Bearing Latitude Departure D. M. D. Areas North South East West North South o +oo S5627E 217.36 827.78 469.58 102,068 3 + 93.3 N6385E 176.71 355.73 1153.09 203,763 7 + 90.5 S0820E 620.78 90.93 1599.75 993,093 14 + 17.9 N7532W 218.08 845.32 845.36 184,856 22 + 90.9 N0905E 443.47 70.90 70.90 31,442 27 + 40.0 Totals 419,561 l,095,16i Applying Rules 2 and 3, the computations for the D.M.D.'s listed above are as follows: D.M.D. of course E = the departure of course E = 70.90 D.M.D. of course A= (70.90) + (70.90 + 327.78) = 469.58 D.M.D. of course B = (469.58) + (327.78) + (355.73) = 1153.09 D.M.D. of course C = (1153.09) + (355.73) + (90.93) = 1599.75 D.M.D. of course D = (1599.75) + (90.93) + (845.32) = 845.36. This should. equal the departure of this course (845.32) and if the survey is unbalanced will be in error by the same amount as the departures fail to balance. The various north and south areas according to Rule 4 will be found as follows: . Course A, (469.58) (217.36) = 102,068 Course B, (1153.09) (176.71) = 203,763 Course C, (1599.75) (620.78) = 993,093 Course D, (845.36) (218.08) = 184,356 Course E, (70.90) (443.47) = 31,442 As the distances are given in feet, the area will be in square feet. The net area a ccording to Rule 5 is as follows: A _ (1,095,161) (419,561) _ 337 800 ft rea _ . 2 , sq. . and as there are 43,650 square feet in one acre, the area in acres will be 337,800 43 , 560 = 7.755 Acres . 316 25
PAGE 28
â€¢ â€¢ â€¢ G. E. 21 NOTES 317. The basis of the D.M.D. method of finding areas may be readily discerned from the following discussion in which meridian distances instead of double meridian distances are used. As previously stated, the meridian distance of any course is the perpendicular distance from the meridian to the midpoint of the course. FIG. 25 From Fig. 25 Area of ABC = (Area of dBCm) (Area of dBA) (Area of ACm) (gh) (dm) (ef) (Ad) (jk) (Am) _ (Mer. Dist. of BC) (Lat. of BC) (Mer. Dist. of AB) (Lat. of AB) (Mer. Dist. of AC) (Lat. of AC) Using double meridian distances: Twice area ABC = (DMD of BC) (Lat. of BC) (DMD of AB) (Lat. of AB) (DMD of AC) (Lat. of AC) And for any figure of more than three sides: Twice the Area= (DMD of each course) (Lat. of each course) (It will be observed that the above statement is in accord with Rules 4 and 5 on Page 316. The advantage of using double meridian distances instead of simply the meridian distances may be seen by examination of the following equation: Mer. Dist. of = [0~;:~~:!~ ]+[pre;;~~!c~~rse ] + [ n~;~t~i:se] any course course 2 2 All positive All positive W depts. are Neg. W depts. are Neg. Note that two terms of the above equation must be divided by 2 for each meridian distance computed. Using DMD's, these two operations are eliminated and a single division by 2 of the final "double" area is all that is required. The saving in time and the elimination of the possibility of errors are therefore the two principal reasons for using DMD's rather than "MD's" in computing areas . 317 26
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â€¢ â€¢ â€¢ OTES SECTION 4 DETERMINING THE DIFFERENCE IN ELEVATION 41. Leveling. The solution of m ny problems depend upon knowing the differenc e in elevation of various point , and the field work neces ary for this is known as ifferential levelin . T o methods are available to the engineer, Direct Leveling and Trigonometric L veling, of which only the former is considered in this course. The Elevation of any point is its ertical distance above some reference or datum plane. This datum plane may be assumed if the results of the leveling do not need to be efer need to other work. If, however, it is desirable to use the results with the el vations of other points, a common datum plane should be used, and this plane i normally the mean sea level or the normal level of the ocean at mean tide. Thus, if the elevation of Mt. Rainier is given as 14,409 feet, it indicates a height of 14,409 feet above mean sea le el, and is 2,150 feet higher than some other peak ith an elevation of 12,259 feet. 4 2. Definitions. Bench Mark (BM). A point of established or known elevation. (May be perman nt or tempo ar . Elevation ( v . The distance (vertic abo some datum plane. Backsi ht . A si h in any 1rection) at some point of known elevation, or v hose elevation s Just been determined. Foresi t (FS). A sight (in any direction) at some point whose elevation is de sired. urning Point TP . An auxiliary point u ed as a temporary bench mark after the el m ed for a new setup. (In orde to be used as a BM its elevation must be determined by a foresight; a turning point, therefore will always be us d twice, fir t from the 1st setup which will be a foresight, and second from the next setup, which will be a backsight). Height of Instrument (HI). The elevation of the line of sight. 43. The Engineer's Level and Level Rod. The Engineer's level is simply a telescope fitted with a horizontal cross hair to form a line of ight, and a spirit level to make this line of sight horizontal; a tripod and leveling screws and other minor features complete the instrument. The level is not set up over a point, as is the tran it, but is set at any random point from which the back sight and desired fore sight may be seen. The level rod is raduated into feet and hundredths and may be a selfreading rod (by the levelman) or a target rod (read by the rodman). The selfreading rod will be used in G. E. 21. Figure 26 represent a portion of a selfreading rod, the cross hair at A reading 4.02, at B, 4.12 and at , 3.95. (A common error i to read this 4.95 because the la ge red "4" is so evident. tt....., ...... ~A Red ++1111111c Fig. 26 41 27
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/~Sefup _fH./. = /02.49~ _ 2.49 7f)2, !0.81 Ete/~fe\,~ ~::::: Sia /35~ f/Z /:5e Bev ,f B.11 ?.49 102.49 /00.tJO A 7.02 95.47 T?; ,r, /. 38'/t 93.56 /0. g'/ 9/.68 B 2./.5 9/.4/ C 8.72 14.84 8.24* /00.39 /.4/* 9Z.l5 D 4./9"' 96.ZO * '2.6/ /64(~ â€¢ 3q/Selvp . f:l.t._j. ""/00:.3.2.::l zt/ Setup /lH. /. = 93.56j 2 ./5 44 8.7Z Differential Leveling : Field work and notes are necessary to determine the elevations of points "A," "B," "C ' and "D." Note: A "Backsight" (BS) is a sight on a point whose elevation is known or which has just been determined. A "Foresight" (FS) is a sight on a point whose elevation is desired. FIG. 27 â€¢ 4.19 â€¢ c;") t.%.1 ,:..:, 1l z 0 8 t_:?:j UJ
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â€¢ â€¢ â€¢ G. E. 21 NOTES 45. Using the Level, (Differential Leveling). The actual setting up of the instrument will be demonstrated by your instructor in the first field period with the level. After the instrument has been leveled, the first sight is at a bench mark in order to determine the height of the instrument (HI). Let it be assumed that we desire the elevation of points A, B, C, and D of Figure 27. The backsight (BS) on the bench mark (BM) whose elevation was 100.00 is 2.49 which, added to the elevation of the bench mark gives 102.49 as the height of the instrument (HI). The level is turned around and a foresight (FS) is taken on the rod held at A, and if this reads 7.02, the elevation of A will be 102.49 (the HI) minus 7.02 (the FS) or 95.47. Now if the rodman moves on to point B, the instrumentman finds that his line of sight passes above the top of the rod and it will be necessary for the rodman to return to some point where the rod can be read through the level. This point is called a turning point (TP) and the foresight on the turning point of 10.81 when subtracted from the height of the instrument will give the elevation of the turning point just as such a procedure gave the elevation of point A. The elevation of the (TP) then will be 102.49 minus 10.81 or 91.68. The instrumentman then picks up the level and moves ahead, setting up at any location where he can take a low reading on the rod. The procedure thereon repeats itself inasmuch as the next sight becomes a backsight at the (TP) whose elevation has just been determined. In other words the (TP) becomes a temporary bench mark each time the instrument is moved. The level notes are as recorded on this figure (also see 21L1). The difference between the summation of the foresights and backsights of the turning points plus the original backsight and the final foresight (the starred figures on the level notes in Figure 27), should equal the difference in elevation between the original and final sights, i.e., [10.81 + 1.41 + 4.19] [2.49 + 1.88 + 8.24] should equal 100.00 96.20 or 16.41 12.61 = 3.80. 46. Hints on the Use of the Level. 1. Have the head of the tripod approximately level when setting up. 2. See that the rod is held vertical when taking a sight. 3. See that the rod is always extended to its full length . 4. Check the level bubble often, especially when taking a turning point.~~5. See that the turning point is some solid object. 6. Check on every point of known elevation available. 7. Have the rodman slowly raise the rod to read the foot mark if it is not in the field of sight, or if the rod is held very close to the level, look along the side of the telescope to get the "foot reading." 8. Make the foresights and backsights on all turning points approximately equal in length to compensate errors due to the level being out of adjustment. 9. Read the rod carefully and record the readings correctly, and in the proper column. 10 .Always compute the elevations as you go along. Only the greenest of beginners wait until after the field work to compute the notes . 45 29
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â€¢ â€¢ â€¢ G. E. 21 NOTES 47. Profile Leveling. In differential leveling the objective was to determine the el evations ( or the difference in elevation) between the various points, such as points A, B, C, and D, of Figure 27, while profile leveling has as its objective the determination of the changes in elevation of the surface of the ground along some definite line such as the center line of a proposed highway, transmission line, or new sewer. The field work is preliminary to the plotting of this ground line on profile paper, where usually the vertical scale (elevations) is greater than the horizontal scale (the chained distances) in order to emphasize these changes in slopes. The profile becomes the framework or basis of design of numerous problems such as highway and railroad location, irrigation and power canals, transmission lines, etc. The actual field work is similar to that of differential leveling, but in order to plot the true slope of the ground it is necessary to determine the elevation of all breaks in the slope and to determine the stationing of all such breaks. Inasmuch as the loca tion of physical features such as railroads, canals, streets, etc., may have an important bearing in the design to follow, it becomes necessary to determine their eleva tions and stationing as well as the breaks in the ground. On a long profile over some determined center line, it is customary to take the elevations at each station, the stationing and elevation of all breaks in the ground slope, and the stationing and elevation of all physical features crossed by the center line or adjacent to the center line which may have a bearing on the design. If a break in the ground slope occurs close to a station, the elevation of the station may be omitted provided it is not a transit (angle) point. 48 Profile Level Notes Profile for Sewer Report Date Party: Brown Weather Smith U. of W. Campus Level No. 30 Jones Station B.S. H.I. F.S. Elev. B.M. 1 5.46 118.87 113.41 N. W. Co. top step Engr. Hall. o +oo 6.25 112.62 Top of ManholeStreet Grade. 0 + 00 104.12 Bot. M. H. 8.50' below top. 0 + 57 6.12 112.75 End of Pavement. 1 +oo 8.07 110.80 2+00 9.55 109.32 T.P. 1 1.42 107.89 12.40 106.47 s +oo 3.22 104.67 3 + 85 4.44 103.45 Angle point. (No. 1) 6 +02 5.02 102.87 Base of west rail. Dist, bet. rails 5.2' B.M. 34 7.33 100.56 NW top post. R.R. Bridge. Elv. 100.55 6+25 6.50 101.39 5+65 11.40 96.49 T.P. 2 etc. (Left side of field book) (Right side of field book) 49. Precision of Leveling. The following maximum allowable errors in checking are suggested. (Values are in feet). Class 1. Rough Leveling. + 0.4 '\ldistance in miles. Class 2. Ordinary Leveling + 0.1\jdistance in miles. Class 8. Accurate Leveling. + 0.05\jdistance in miles. Class 4. Precise Leveling. + 0.02\jdistance in miles . 47 30
